The existence of continuous selection for a lower semicontinuous multifunction reduces problems of existence of solutions in differential inclusion involving such multifunction into a corresponding differential equation. In this paper, an extension of Michael selection theorem to a non-commutative setting is established. The result is then applied in the establishment of the existence of solutions of quantum stochastic evolution inclusion. The quantum stochastic evolution inclusion has its coefficients to be operator-valued stochastic processes which are hypermaximal monotone and lower semicontinuous multifunctions.